QTreeView с QStandardItemModel: как реализовать собственную модель сортировки

Вы должны создать класс, наследуемый от QSortFilterProxyModel, и перезаписать метод lessThan:

import sys
from PyQt5 import QtCore, QtGui, QtWidgets

# fake _human_key
# https://stackoverflow.com/a/5254534/6622587
import re
def _human_key(key):
    parts = re.split(r'(\d*\.\d+|\d+)', key)
    return tuple((e.swapcase() if i % 2 == 0 else float(e))
            for i, e in enumerate(parts))

class HumanProxyModel(QtCore.QSortFilterProxyModel):
    def lessThan(self, source_left, source_right):
        data_left = source_left.data()
        data_right = source_right.data()
        if type(data_left) == type(data_right) == str:
            return _human_key(data_left) < _human_key(data_right)
        return super(HumanProxyModel, self).lessThan(source_left, source_right)


class StyledItemDelegate(QtWidgets.QStyledItemDelegate):
    def displayText(self, value, locale):
        if isinstance(value, QtCore.QDateTime):
            return value.toString('MM/dd/yyyy hh:mm A')
        return super(StyledItemDelegate, self).displayText(value, locale)

class App(QtWidgets.QWidget):
    COL_ID = 0
    MAIL_RANGE = 4
    ID, FROM, SUBJECT, DATE = range(COL_ID, MAIL_RANGE) # four elements: 0, 1, 2, 3

    def __init__(self):
        print("class App, __init__() called.")
        super().__init__()      
        self.left = 100
        self.top = 110
        self.width = 640
        self.height = 240
        self.initUI()

        self.dataView.setSelectionMode(QtWidgets.QAbstractItemView.ExtendedSelection)
        self.dataView.setEditTriggers(QtWidgets.QAbstractItemView.NoEditTriggers)
        self.dataView.setSortingEnabled(True)
        self.dataView.sortByColumn(2, QtCore.Qt.AscendingOrder)
        delegate = StyledItemDelegate(self.dataView)
        self.dataView.setItemDelegate(delegate)        

        for i in range(0, 2):
            self.dataView.resizeColumnToContents(i)

        self.pbEdit = QtWidgets.QPushButton(self)
        self.pbEdit.setText("Edit")
        self.pbEdit.move(400,0)
        self.pbEdit.show()

        self.pbDel = QtWidgets.QPushButton(self)
        self.pbDel.setText("Delete")
        self.pbDel.move(500,0)
        self.pbDel.show()

        # connect handlers
        self.dataView.doubleClicked.connect(self.on_dataView_doubleClicked)
        self.pbEdit.clicked.connect(self.on_pbEdit_clicked)

    def open_dialog(self):
        rows = set(ix.row() for ix in self.dataView.selectedIndexes())  
        for row in rows:
            ix = self.dataView.model().index(row, App.COL_ID)
            my_id = ix.data()            
            self.create_dialog(my_id)

    def on_dataView_doubleClicked(self):
        print("class app, on_dataView_doubleClicked() called.")
        self.open_dialog()

    def on_pbEdit_clicked(self):
        print("class app, on_pbEdit_clicked() called.")
        self.open_dialog()

    def create_dialog(self, _id):
        print("dialog called for {}".format(_id))
        myDlg = QtWidgets.QDialog(self)
        lbl = QtWidgets.QLabel(myDlg)
        lbl.setText("Hello id: {}".format(_id))
        # myDlg.exec_()  #  <- modal
        myDlg.show()     #  <- non-modal
        myDlg.resize(300,200)


    def initUI(self):
        print("class App, initUI() called.")
        self.setGeometry(self.left, self.top, self.width, self.height)

        self.dataGroupBox = QtWidgets.QGroupBox("Inbox")
        self.dataView = QtWidgets.QTreeView()
        self.dataView.setRootIsDecorated(False)
        self.dataView.setAlternatingRowColors(True)        

        dataLayout = QtWidgets.QHBoxLayout()
        dataLayout.addWidget(self.dataView)
        self.dataGroupBox.setLayout(dataLayout)

        model = self.createMailModel(self.dataView)
        proxy = HumanProxyModel(self)
        proxy.setSourceModel(model)
        self.dataView.setModel(proxy)
        self.addMail(model, 1, '[email protected]', 'Zabel', QtCore.QDateTime.fromString('03/25/2017 02:05 PM', 'MM/dd/yyyy hh:mm A'))
        self.addMail(model, 2, '[email protected]', 'Schneider', QtCore.QDateTime.fromString('02/02/2017 03:05 PM', 'MM/dd/yyyy hh:mm A'))
        self.addMail(model, 3, '[email protected]', 'anabel', QtCore.QDateTime.fromString('01/01/2017 04:05 PM', 'MM/dd/yyyy hh:mm A'))
        self.addMail(model, 4, '[email protected]', 'Arachno', QtCore.QDateTime.fromString('03/25/2017 02:05 PM', 'MM/dd/yyyy hh:mm A'))
        self.addMail(model, 5, '[email protected]', 'Öztürk', QtCore.QDateTime.fromString('02/02/2017 03:05 PM', 'MM/dd/yyyy hh:mm A'))
        self.addMail(model, 6, '[email protected]', 'Becker', QtCore.QDateTime.fromString('01/01/2017 04:05 PM', 'MM/dd/yyyy hh:mm A'))

        self.dataView.setColumnHidden(App.COL_ID, True)

        mainLayout = QtWidgets.QVBoxLayout(self)
        mainLayout.addWidget(self.dataGroupBox)
        self.show()


    def createMailModel(self,parent=None):
        model = QtGui.QStandardItemModel(0, self.MAIL_RANGE, parent)

        model.setHeaderData(self.ID, QtCore.Qt.Horizontal, "ID")
        model.setHeaderData(self.FROM, QtCore.Qt.Horizontal, "From")
        model.setHeaderData(self.SUBJECT, QtCore.Qt.Horizontal, "Subject")
        model.setHeaderData(self.DATE, QtCore.Qt.Horizontal, "Date")
        return model

    def addMail(self, model, mailID, mailFrom, subject, date):
        model.insertRow(0)
        model.setData(model.index(0, self.ID), mailID)
        model.setData(model.index(0, self.FROM), mailFrom)
        model.setData(model.index(0, self.SUBJECT), subject)
        model.setData(model.index(0, self.DATE), date)        

if __name__ == '__main__':    
    app = QtWidgets.QApplication(sys.argv)
    ex = App()
    sys.exit(app.exec_())